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Câu 1 : \(\frac{x}{2}=\frac{2y}{5}=\frac{4z}{7}\)\(\Rightarrow\)\(\frac{1}{4}.\frac{x}{2}=\frac{1}{4}.\frac{2y}{5}=\frac{1}{4}.\frac{4z}{7}\)\(\Leftrightarrow\)\(\frac{x}{8}=\frac{y}{10}=\frac{z}{7}\) \(\Rightarrow\)\(\frac{3x}{24}=\frac{5y}{50}=\frac{7z}{49}=\frac{3x+5y+7z}{24+50+49}=\frac{123}{123}=1\)
\(\frac{3x}{24}=1\Rightarrow3x=24\Rightarrow x=8\)
\(\frac{5y}{50}=1\Rightarrow5y=50\Rightarrow y=10\)
\(\frac{7z}{49}=1\Rightarrow7z=49\Rightarrow z=7\)
Vậy x,y,z lần lượt là 8,10,7
Ta có: \(\frac{x-18}{2018}=\frac{x-17}{2017}\)
\(\Rightarrow\left(x-18\right).2017=\left(x-17\right).2018\)( tính chất của 2 tỉ số bằng nhau )
\(2017x-2017.18=2018x-2018.17\)
\(2018.17-2017.18=2018x-2017x\)
\(\left(2017+1\right).17-2017.\left(17+1\right)=x\)
\(2017.17+17-2017.17-2017=x\)
\(x=-2000\)
Vậy \(x=-2000\)
\(\frac{x+1}{99}+\frac{x+2}{98}=\frac{x-1}{101}+\frac{x-2}{102}\)
\(\Rightarrow\left(\frac{x+1}{99}+1\right)+\left(\frac{x+2}{98}+1\right)=\left(\frac{x-1}{101}+1\right)+\left(\frac{x-2}{102}+1\right)\) ( cộng cả 2 vế thêm 2 )
\(\frac{x+100}{99}+\frac{x+100}{98}=\frac{x+100}{101}+\frac{x+100}{102}\)
\(\Rightarrow\frac{x+100}{99}+\frac{x+100}{98}-\frac{x+100}{101}-\frac{x+100}{102}=0\)
\(\left(x+100\right).\left(\frac{1}{99}+\frac{1}{98}-\frac{1}{101}-\frac{1}{100}\right)=0\)
Ta có: \(\frac{1}{99}+\frac{1}{98}-\frac{1}{101}-\frac{1}{100}\ne0\)
\(\Rightarrow x+100=0\)
\(x=-100\)
Vậy \(x=-100\)
a, \(\frac{x-18}{2018}=\frac{x-17}{2017}\)
=>\(\frac{x-18}{2018}+1=\frac{x-17}{2017}+1\)
=>\(\frac{x-18+2018}{2018}=\frac{x-17+2017}{2017}\)
=>\(\frac{x+2000}{2018}=\frac{x+2000}{2017}\)
=>\(\frac{x+2000}{2018}-\frac{x+2000}{2017}=0\)
=>\(\left(x+2000\right)\left(\frac{1}{2018}-\frac{1}{2017}\right)=0\)
Mà \(\frac{1}{2018}-\frac{1}{2017}\ne0\)
=>x+2000=0 => x=-2000
b,
=>\(\frac{x+1}{99}+1+\frac{x+2}{98}+1=\frac{x-1}{101}+1+\frac{x-2}{102}+1\)
=>\(\frac{x+1+99}{99}+\frac{x+2+98}{98}=\frac{x-1+101}{101}+\frac{x-2+102}{102}\)
=>\(\frac{x+100}{99}+\frac{x+100}{98}=\frac{x+100}{101}+\frac{x+100}{102}\)
=>\(\frac{x+100}{99}+\frac{x+100}{98}-\frac{x+100}{101}-\frac{x+100}{102}=0\)
=>\(\left(x+100\right)\left(\frac{1}{99}+\frac{1}{98}-\frac{1}{101}-\frac{1}{102}\right)=0\)
Mà \(\frac{1}{99}+\frac{1}{98}-\frac{1}{101}-\frac{1}{102}\ne0\)
=>x+100=0 => x=-100
\(\frac{2030-x}{15}+\frac{2041-x}{13}+\frac{2048-x}{11}+\frac{1961-x}{9}=0\)
\(\Leftrightarrow\frac{2030-x}{15}-1+\frac{2041-x}{13}-2+\frac{2048-x}{11}-3+\frac{1961-x}{9}+6=0\)
\(\Leftrightarrow\frac{2015-x}{15}+\frac{2015-x}{13}+\frac{2015-x}{11}+\frac{2015-x}{9}=0\)
\(\Leftrightarrow\left(2015-x\right)\left(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\right)=0\)
Mà \(\frac{1}{15}+\frac{1}{13}+\frac{1}{11}+\frac{1}{9}\ne0\)
\(\Rightarrow2015-x=0\Leftrightarrow x=2015\)
Ap dung tinh chat day ti so bang nhau Ta co :
\(\frac{x}{9}=\frac{z}{7}=\frac{y}{8}=\frac{t}{6}=\frac{y-t}{8-6}=\frac{70}{2}=35\)
Suy ra x= 35 . 9 =315
z =35.7=245
y = 35.8=280
t=280-70=210
Vay x=315,y=280,z=245,t=210
Chuc ban hoc tot
Áp dunhj tính chất của dãy tỉ số bằng nhau ta có :
\(\frac{x}{9}=\frac{y}{8}=\frac{z}{7}=\frac{7}{6}=\frac{y-7}{8-6}=\frac{70}{2}=35\)
\(\Rightarrow\frac{x}{9}=35\Rightarrow x=315\)
\(\frac{y}{8}=35\Rightarrow y=280\)
\(\frac{z}{7}=35\Rightarrow z=245\)
\(\frac{t}{6}=35\Rightarrow t=210\)
Study well
Ta có:
\(\frac{y+z+t}{x}=\frac{z+t+x}{y}=\frac{t+x+y}{z}=\frac{x+y+z}{t}\)
\(=\frac{2\left(x+y+z+t\right)}{x+y+z+t}\left(tcdtsbn\right)\)=2
\(\Rightarrow y+z+t=2x;z+t+x=2y;\)
\(t+x+y=2z;x+y+z=2t\)
Tu do de CM x=y=z=t
Khi do
\(A=1+1+1+1=4\)
Xet \(x+y+z+t=0\)
\(\Rightarrow A=\frac{x+y}{z+t}+\frac{y+z}{t+x}+\frac{z+t}{x+y}+\frac{t+x}{y+z}=-1-1-1-1=-4\)
Xet \(x+y+z+t\ne0\)
\(\Rightarrow\frac{y+z+t}{x}=\frac{z+t+x}{y}=\frac{t+x+y}{z}=\frac{x+y+z}{t}=\frac{3\left(x+y+z+t\right)}{x+y+z+t}=3\)
\(\Rightarrow x=y=z=t\ne0\)
\(\Rightarrow A=4\)
\(\frac{x+1}{2}=\frac{18}{x+1}\Rightarrow\left(x+1\right)^2=36\)
Nên \(x+1=6\Rightarrow x=5\)
\(x+1=-6\Rightarrow x=-7\)
Vậy x=5 hoặc x=-7